For digital photography, fewer filters are necessary than for 35mm film, since many types of color correction or special effects can be generated in postprocessing.

However, a number of filters are or can be useful:

- Polarizing filters: to darken blue skies (the strongest effect is at a right angle with respect to the sun), or to reduce reflections in glass (e.g., taking a photograph through window), as well as reflections from water and foliage. For digital cameras this needs to be a circular-polarizing filter (CPL).
Note that with ultra-wide angle lenses a CPL filter will cause uneven darkness of the sky due to the large angle covered, and therefore changing strength of the polarizing effect (see example, example2 ). However, beneficial effects on foliage will still work fine.

Note that many polarizing filters reduce the amount of light passed by at least 1 f-stop, and have different effects depending on orientation, so are not useful as general protectors. Some newer filters (e.g., Hoya HD CPL) seem to have less light loss than others (e.g., only about 1 stop, see transmission curve here).
Note that some of the super multicoated CPL filters seem to give color casts (see here , and here).

- Neutral density gradient filters: to adjust for bright skies in landscape photography (e.g., this thread). The sensor of a camera has a limited dynamic range, and bright skies will be overexposed, while buildings and/or landscape are too dark. Neutral gradient filters can reduce such strong differences. As alternative several pictures of the same scene can be taken with different exposure levels, which are then combined in postprocessing. However, this usually requires static scences with no movement (see also high dynamic range photography).

- Neutral density filters (ND): to be able to take long exposure times even when the scene is bright, e.g., to blur water, people or cars. For some more detailed description see here. A number of manufacturers make variable ND filters. These are basically two polarisers sandwiched together that can be rotated against each other. You can achieve a similar effect by using two normal polarisers together, see this Digital ImageMaker article , and this article at DPS (Digital Photography School). As noted above under color cast, if the ND filter passes IR, magenta color casts can occur.

- IR filters: special filters for Infrared photography, see the infrared links.

- UV filters/Protection filters: There are huge debates about pros and cons of such filters on the internet. I have no interest in engaging in this, everybody can choose themselves. Here is just some information that may be useful.

UV filters had an important function in film days in order to filter strong UV light, since film was much more sensitive to UV light than the sensors of modern digital cameras. Further, most modern lenses do not transmit much UV light anyway (See also lens transmission curves). Thus, UV filters can really just be considered protection filters for the lens.
Protection filters are clear filters for lens protection. Firstly, irrespective of a filter or not, a hood should be used whenever possible. It helps prevent flares from stray light, etc., but will also shield the front element from various kinds of impact. Clear protector filters do not filter UV, but essentially they are very similar to the UV filters.
Protection filters can help to protect the front element from dust and dirt (e.g., beach). Depending on the kind of dust, if it is stuck and hard like sand grains, there is the potential to damage the front lens or coating during cleaning. In general, it is a good idea to use blowers rather than wipes as much as possible for lens cleaning (scratching/wiping a sand grain on glass is not a good idea). Depending on the lens design, a front filter can also help protect against dust entering the lens. The Canon EF-S 17-55 seems notorious for sucking dust behind the front element, and apparently a filter can help. A filter may be necessary to complete the weather sealing on some of the older Canon L tele lenses. Also other lenses maybe have front areas, where dirt can enter. E.g., during zooming of the Canon EF-S 10-22 mm lens the inner lens barrel is moving back and forth inside the outer barrel that holds the filter. Dust would be difficult to remove in the narrow edge at the corner, and the forward/backward movement during zooming could work dust inside the lens. Thus, a filter can eliminate this possible entry point of dust into the lens. Scratches to front elements can accidently happen (see this thread). So, depending on where and how one uses a lens, a UV or protector filter can be useful.

Impact on image quality

Two aspects are of major concern with filters: impact on image quality (resolution), and additional flare/loss of contrast due to the extra glass-air interfaces.

Image quality: Filter tests by lensrentals and Lester Wareham show that good quality filters do not significantly degrade sharpness. However, it is clear that bad filters do impact quality, and the effect is more pronounced at longer focal lengths. Most complaints on forums are with cheap filters on tele lenses, e.g., 100-400 or 400mm lenses. 
Flare: If one decides to get a filter, one should get a multicoated filter, see also the lenstip tests below. Non-coated filters increase flare, e.g., thephotoforum, photo.net, EyvindNess_samples, and see especially Lester Wareham's filter tests. The Holding Tank filter tests also show little difference between a Hoya Digital Pro1 UV and a B+W MRC (Holding Tank filter test).

There habe been reports that some filters may cause issues such as changed AF or bad bokeh on some tele lenses, e.g. the 100-400 L, but it's not clear if is this is simply due to a bad filter that also has IQ problems, or if that is a separate issue. Further, long lenses, depending on background, can have a busy bokeh, so a rigorous test with and without filter would be necessary.

Filter choices

needs updating....

For lens protection: Here one needs a circular protector or UV filter that fits the front of the lens.

Hoya have a somewhat bewildering array of filters, which is unfortunately not that well described on their home page:
Green Packaging = uncoated. Some UK resellers sell them as monocoated. (??) Poor, not recommended (sample shown here )
Blue/Purple Packaging = double coated (1 coat each side, monocoated), made in Japan. Some filters, such as e.g., CPL and special effect filters (star etc.) are not coated.
HMC=Multicoat = 3 layers each side, 5mm thick?. There are UV(o) and UV(N) versions. 97% transmission.
UMC=Ultra thin = slim 3mm, except polarizer which is 5mm, no front thread (should be discontinued)
Super HMC (SMC, S-HMC) = 6 layers each side for UV, Skylight filters, 99.7% transmission, no front thread (discontinued ?)
Super HMC (SMC) Pro 1 = 6 layers each side, slim, 3mm thin (polarizer is 5mm with 7 layers on rear), with front thread - might be discontinued now, though still available.
Pro 1 Digital seems to be 3 and 3 front and back(?), 98% transmission, slim build 3mm, polarizer 5mm, front thread for other filters.
HD, filters (May 2008) much harder glass, more resistant coating, slim build (4mm, CPL 5mm), with front threads. CPL lets through more light, almost 90% (see Hoya , and optyczne.pl, see links below). The new coatings are reportedly easier to clean that the SMC and digital Pro1 coatings.
HD2, new filters, supposedly the same as HD, new package.

Kenko is distributed in the USA by the same conglomerate as Hoya and Tokina, see also this thread. Kenko is supposedly the brand under which Hoya filters are distributed, e.g., in Japan - though I still have not found proof of that (see this thread\). Kenko is definitively the same company as Tokina Kenko-Tokina. Hoya also bought out Pentax , as of 31. March 2008 the merger should be complete. In 2011 Hoya sold Pentax to Ricoh.
Kenko filters, at least the digital Pro1 series filters should be similar to the Hoya digital Pro1 series - one notices very similar packaging. Kenko is or used to be primarily distributed in Japan/Asia, although the digital Pro1 series are showing up in European and American stores. On ebay and some other places, Kenko filters can be obtained at somewhat lower prices than Hoya filters. Note that Hoya has a large glass-works in Thailand with a capacity of 60 Million glass discs per year for computers and cameras that probably supplies a lot of glass to Japan. However, the UV filter tests at Lenstip show that the coatings of the Kenko and Hoya digital Pro1s are different, so they don't seem to be identical, even though the glass is probably the same.
New filters: Kenko E series
Kenko zeta: 99.7% transmission of coating, ~7 coatings, seems similar to Hoya SHMC, UV 4mm thick, CPL 5mm thick, with front threads. Some claims that they are the same or similar as Hoya HD (not confirmed).


B+W filters offer high quality MRC coated filters, which have a reputedly stronger and easier to clean coating than the Hoya SMC and digital Pro1 filters. Made from Schott glass. Based on these threads thread 1 thread2, B+W make brass mounted filters (made in Germany), but for Asia they (also ?) produce "alloy" (not brass) mounted filters. Optical quality should be the same though. Different rims are available, such as F-Pro (4mm for UV, 6-7?? for CPL), slim with no front thread for UWA (3mm for UV, 5mm CPL?), and the new XS-Pro, which are slim with front thread (3mm UV, 5? for CPL). MRC coating gives 0.5% reflection.

Heliopan is another German manufacturer of filters from Schott glass. They also have a coating (SH-PMC) apparently similar to the B+W MRC.

Tiffen , USA filters. However some Tiffen UV seem to be the same as some cheap generic filters, see this thread, and the standard ones are not multicoated. They do offer though also multicoated filters now.

Check also this comparison at the Holding Tank

Graduated neutral density (GND) filter or occasionally called Neutral density graduated (NDG) filter:

The "square filter" system is most useful for this (rather than a circular one in a filter thread) You only need one set of filters for various lenses and you can move the filter up and down within the folder to adjust the zone of transition. Several companies offer such filters. The Cokin, Hitech, Singh-Ray, and Lee GNDs are all made from optical resin.

ND filters page.

Hitech filters by Formatt : CR39 dyed substrate, according to forum reports more color neutral - see also the filter tests section here for transmission spectra. The "P" size filter is now most likely 84 x 109mm (see SRB~Griturn Hitech filters below). Various online sources reported: 85 x 110mm (or 107, depending on source). Older versions of the Hitech filters seem to have been 85mm wide (1mm wider than the Cokin P filter holder, and will not fit easily - some have sanded them down to fit). An email I got from Hitech in March 2008 states that they make all their filters now 84mm wide. Hitech also has 100 x 125mm and 100 x 150mm filters. The nice thing is that they offer both soft and hard transition neutral density gradients in a number of densities. A kit with 3 common 85mm filters is 35 pound incl. VAT. TeamWork also resells the neutral density gradient kit.

SRB~Griturn also carry their own variant of the Hitech filters cut to 84mm (confirmed by email from their tech support). They have also the soft and hard gradient options as well as the different densities. They are a bit more expensive, because no kit is offered. They also have some of their own filters that fit Cokin A and P formats. I ordered (Aug. 2008) soft and hard transitions ND gradients and a ND (4 stop) filter. The filters were packaged as Hitech filters, and are probably straight Hitech filters without further modification, since Hitech now are also 84mm. Size is 84mm by 109mm for the gradient, the ND is square. Corners are diagonally cut off to make insertion into the holder easier.

Kood has Cokin P and A format type filters as well.

Singh-Ray has Cokin P sized and 100 x 150 (4x6inch) resin filters, rather expensive.

Lee has 100 x 150mm resin filters, rather expensive, but excellent reputation.

Tiffen has square filters in many different large format sizes (e.g., 2 x 2 inches, 4 x 5 inches).

Tian Ya (ebay), Chinese filters, 84 x 100 mm


Stuck filters
Apply pressure evenly (don't squeeze the filter), put a rubber band around for more grip, or use rubber gloves.
B+W filters have front ribbing that interlocks with the B+W CPL and makes them stuck, so try to avoid using two at the same time, see this thread . Hoya Digital Pro1 have no front ribbing (only sides), and Hoya HD has front ribbing, but the surface is smoother than B+W.

Cleaning
At least some multicoated filters can be difficult to clean.
Here are some suggestions, how to clean filters.
Note: it is probably not a good idea to clean the resin based filters (Cokin, Hitech, Lee, Singh-Ray) with liquids - especially ones containing organic solutions as it might damage the filter.

Links
Bob Atkins' comments on filters for Digital Cameras. Bob Atkins' filter transmission curves.
Lenstip test of UV filters (e.g., B+W, Hoya, Kenko, Heliopan, Hama, Marumi, Tiffen) at (www.lenstip.com). This is a translation of the original test on the Polish web site www.optyczne.pl.
Lenstip test of CPL filters (e.g., B+W, Hoya, Kenko, Heliopan, Hama, Marumi, Tiffen). Original CPL test at www.optyczne.pl.
Tests of Hoya HD and Cokin CPLs at lenstip and at www.optyczne.pl. (polish).
Tests of Hoya HD, Fomei, King Digital, Samyang, and Cokin UV filters at lenstip and at www.optyczne.pl (polish).
Lester Wareham's Holding Tank has some filter tests on flare, showing different coatings behave differently on different lenses.
Traumflieger CPL test of 5 filters, in german, but pictures are obvious.